X^2-y^2=48 and x-y=2. The solution to the given system of equations is (x,y). What is the value of x + y?

Answers

Answer 1

Answer:

24

Step-by-step explanation:

We have a system of equations, so we can start with the second equation:

[tex]x-y=2[/tex]

And move y to the other side to isolate x:

[tex]x=2+y[/tex]

Now we can replace x into the first equation:

[tex](2+y)^{2} -y^{2} =48\\ (2+y)(2+y)-y^{2} =48\\ 4+4y+y^{2} -y^{2} =48[/tex]

Notice that we can cancel out the y squared terms:

[tex]4+4y=48\\ 4y=44\\ y=11[/tex]

Now we just need to find x by replacing y into the second equation:

[tex]x-11=2\\ x=13[/tex]

And finally, add them:

[tex]x+y=11+13\\ x+y=24[/tex]

Hope this helps.

Answer 2

Answer:

x= 13

y=11

x^2 - y^2 = 48        and       x - y = 2

                                           x = 2 + y

(2 + y)^2 - y^2 = 48

(2 + y) (2 + y) - y^2 = 4

(4 + 2y +2y + y^2) -y^2 = 48

4 + 4y + y^2 - y^2 = 48

4 + 4y = 48

4y = 48 -4

4y = 44

y= 44/4

y= 11

Plug y back into the original equation:

x^2 - y^2 = 48

x^2 - 11^2 = 48

x^2 - 121 = 48

x^2 = 121 + 48

x^2 = 169

The square root of 169 is 13

So x= 13

x + y

13 + 11 = 24


Related Questions

Luke has a piece of rope that is 3.6 meters long. He cuts the rope into two pieces. One is 1.93 meters long. How long is the other piece of rope?

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the answer is 1.67 because you have to subtract 1.93 from 3.6

Find the area of a regular hexagon with side length of 2 m. Round your answer to the nearest tenth.

Answers

Answer:

12

Step-by-step explanation:

A regular hexagon has 6 equal sides

2 times 6 = 12

Answer:

10.4m²

Step-by-step explanation:

A≈10.39m²

A=33

2a2=3·3

2·22≈10.3923m²

= 10.4m²

Simplify this question

Answers

[tex]3 + \sqrt{ - 12} \\ = 3 + \sqrt{ 2 \times 2 \times - 3} \\ = 3 + 2 \sqrt{ - 3} [/tex]

Hope you could get an idea from here.

Doubt clarification - use comment section.

[tex]\\ \sf\longmapsto 3+√-12[/tex]

[tex]\\ \sf\longmapsto 3+√12i[/tex]

[tex]\\ \sf\longmapsto 3+√2(2)(3)i[/tex]

[tex]\\ \sf\longmapsto 3+2√3i[/tex]

Which of the values shown are potential roots of f(x) = 3x3 â€"" 13x2 â€"" 3x 45? Select all that apply.

Answers

The potential roots of the function are, [tex]\pm1, \ \pm3, \ \pm5, \ \pm9,\ \pm15, \ \pm45,\ \pm \dfrac{1}{3},\ \pm \dfrac{5}{3}[/tex]

And the accurate root is 3 it can be determined by using rules of the rational root equation.

Given that,

Function; [tex]\rm f(x) = 3x^3 - 13x^2 -3x + 45[/tex]

We have to determine,

Which of the values shown are potential roots of the given equation?

According to the question,

Potential roots of the polynomial are all possible roots of f(x).

[tex]\rm f(x) = 3x^3 - 13x^2 -3x + 45[/tex]

Using rational root theorem test. We will find all the possible or potential roots of the polynomial.

[tex]\rm p=\dfrac{All\ the \ positive}{Negative\ factors \ of\ 45}[/tex]

[tex]\rm q=\dfrac{All\ the \ positive}{Negative\ factors \ of\ 3}[/tex]

The factor of the term 45 are,

[tex]\pm1, \ \pm3, \ \pm5, \ \pm9,\ \pm15, \ \pm45[/tex]

And The factor of 3 are,

[tex]\pm1, \ \pm3[/tex]

All the possible roots are,

[tex]\dfrac{p}{q} = \pm1, \ \pm3, \ \pm5, \ \pm9,\ \pm15, \ \pm45,\ \pm \dfrac{1}{3},\ \pm \dfrac{5}{3}[/tex]

Now check for all the rational roots which are possible for the given function,

[tex]\rm f(x) = 3x^3 - 13x^2 -3x + 45\\\\ f(1) = 3(1)^3 - 13(1)^2 -3(1) + 45 = 3-13-3+45 = 32\neq 0\\\\ f(-1) = 3(-1)^3 - 13(-1)^2 -3(-1) + 45 =- 3-13+3+45 = 32\neq 0\\\\ f(3) = 3(3)^3 - 13(3)^2 -3(3) + 45 = 81-117-9+45 =0\\\\ f(-3) = 3(-3)^3 - 13(-3)^2 -3(-3) + 45 = -81+117+9+45 =-144\neq 0[/tex]

Therefore, x = 3 is the potential root of the given function.

Hence, The potential roots of the function are, [tex]\pm1, \ \pm3, \ \pm5, \ \pm9,\ \pm15, \ \pm45,\ \pm \dfrac{1}{3},\ \pm \dfrac{5}{3}[/tex].

For more details about Potential roots refer to the link given below.

https://brainly.com/question/25873992

Answer: ALL OF THEM

Step-by-step explanation:

Martin spent six dollars on four avocados how much money does he spend for two avocados

Answers

Answer:

$3

Step-by-step explanation:

cut the price in half because the amount of items was reduced by half

Answer:

three dollars

Step-by-step explanation:

$6 for 4

$x for 2

6=4

x=2

cross multiply

2×6=4×x

12=4x

Divide through by 4

x= 3

(BRAINLIEST TO THE PERSON WHO HELPS ME WITH THESE THREE QUESTIONS)
Cheryl writes 7 fewer posts than Kevin on a social media site.
Answer the questions to write an algebraic expression. Then evaluate the expression for the given value.
1. Choose a variable to represent the number of posts Kevin writes. Explain why you chose this variable.

2. Which operation (addition, subtraction, multiplication, or division) applies to this situation? Justify your choice.
3. Use your variable and the operation you identified to write an expression for the number of posts Cheryl wrote.

Answers

Answer:

Cheryl's posts + 7 posts =Kevin Posts

K-C=7 or C+7+K I use them because C is Cheryl and K is Kevin

Operation=subtraction or addition because it could be K-C=7 or C+7+K

Cheryl wrote K-7=C posts

Answer:

Cheryl writes 7 fewer posts than Kevin on a social media site.

Answer the questions to write an algebraic expression. Then evaluate the expression for the given value.

1. Choose a variable to represent the number of posts Kevin writes. Explain why you chose this variable. (2 points)

The expression will be P for "of posts Kevin writes." 

2. Which operation (addition, subtraction, multiplication, or division) applies to this situation? Justify your choice. (2 points)

 The operation I will use is subtraction so P-7.

3. Use your variable and the operation you identified to write an expression for the number of posts Cheryl wrote. (3 points)

Subtraction would be the operation and my expression would be ( P-7 ) which would also be ( 21 - 7 )

How many minutes make a hour

Answers

Answer:

60 minutes make an hour

Step-by-step explanation:

Because 1 hour = 60 minutes

60 minutes equal a hour

Complete the slope-intercept form of the linear equation that represents the relationship in the table.

Answers

y = -2x + 5

hope this helps!

97 term of-5,-23,-41

Answers

Answer:

-1147

Step-by-step explanation:

Answer:

-1733

Step-by-step explanation:

-5-96*18 = -1733

Please help me solve for n

Answers

To solve for N, you have to work backwards

1. Take off the absolute sigh

the absolute sign only means that the answer must be positive. So that means N could equal to positive and Negative

2. What is 1x6?

This process is called inverse operation. Where you have division, you have multiplications. The answer is 6.

3. The answer is 6 or negative 6, in the fact that -6 would equal to six in the absolute sign.

I hope this helped! If it's wrong blame me!

In a solid cube made up of smaller black and white cubes. The black and white cubes are at alternate places of the larger cube. How many black cubes are there in the above arrangement?

Answers

There are 168 black cubes in the arranagement.

A cube has 6 faces. Each face of the cube consists of 25 white cubes and 24 black cubes.

To get the number of black cubes in the arrangement, we will use the equation below;

Number of black cubes = Total number of black cubes on a face * number of small cubes along the edgeNumber of black cubes = 24 * 7Number of black cubes = 168

Hence there are 168 black cubes in the arrangement.

Learn more about cubes at https://brainly.com/question/1972490

The equation and graph show the cost to rent movies
from two different companies. The cost is a function of
the number of movies rented.
Which description best compares the two functions?


Answers

Answer:

Hello! Your answer should be there is a higher rate of change at Company 1.

Step-by-step explanation:

Hope this helped! :)

Have a great rest of your day!

                                                   

If m∠2=4x+7 and m∠7=5x-13, find x.

Answers

Answer:

x =20

Step-by-step explanation:

m∠2 ≅ m∠6 because they are corresponding angles

m∠6 ≅ m∠7 because they are vertical angles

∴ m∠2 ≅ m∠7 by substitution

4x+7 = 5x-13

7 = x-13

20 = x

The value of x is 20.

What are vertically opposite angles?

Vertical angles are angles opposite each other where two lines cross.

What are corresponding angles?

Any pair of angles each of which is on the same side of one of two lines cut by a transversal and on the same side of the transversal are corresponding angles.

According to the given question.

We have

m ∠2 = 4x + 7

and m ∠7 = 5x - 13

From the given figure we can say that

m ∠7 = m ∠6...(i)  (because they are vertically opposite angles)

and m ∠6 = m ∠2...(ii)   ( corresponding angles)

From (i) and (ii)

m ∠7 = m ∠2

⇒ [tex]5x - 13 = 4x + 7[/tex]

⇒ [tex]5x - 4x = 7 +1 3[/tex]

⇒ [tex]x = 20[/tex]

Hence, the value of x is 20.

Find out more information about vertically opposite angles and corresponding angle here:

https://brainly.com/question/18296786

#SPJ3

Do now: Balance the following equation.
1.
C₂H₂ + O₂--
+
--->
- CO2 + H2O

Answers

Answer:

C2H2 + 3O2 ---> 2CO2 + 2H2O

Step-by-step explanation:

Which theorem would be used to prove the triangles below as congruent?
A: HL
B: SSS
C: ASA
D: AAA

Answers

Answer:

  A:  HL

Step-by-step explanation:

The hypotenuses of these right triangles are marked congruent.

One leg of these right triangles is marked congruent.

The HL theorem applies.

Answer:

A

Step-by-step explanation:

The hypotenuses of these right triangles are marked congruent.

One leg of these right triangles is marked congruent.

The HL theorem applies.

Tyra, Elle, Tran, and Ann share equally in the rental of a car. If the total cost of the rental is C dollars, which expression represents Tyra's share of the cost?

Answers

Answer:

c/4

Step-by-step explanation:

Since it's equally shared, and the total cost is C, then the answer is c/4

I will report you if you send a link ;-; help correctly.

Answers

Answer:

the correct is 39

Step-by-step explanation:

there is nine number there so the fifth is it and it was in order that helped alot

help me please i cant math

Answers

Answer:

  (b)  3 +x = 12

Step-by-step explanation:

To solve these for x, you would ...

  a) divide by 3

  b) subtract 3

  c) add 3

  d) multiply by 3

The subtraction property of equality says you can subtract the same value from both sides of an equation without affecting the value of the variable(s). It is applicable when you need to subtract a quantity in order to get the variable by itself.

Solving 3 +x = 12 would make use of the Subtraction Property.

Please help me with this question.

Answers

Answer:

aww i help u.....

Step-by-step explanation:

my answer is letter ~~B CAUSE STUDEN BIS CONDYCTION LIKR FREE AT THE SCORED

A TV has a listed price of $900.99 before tax. If the sales tax rate is 6.75%, find the total cost of the TV with sales tax included.
Round your answer to the nearest cent, as necessary.

Answers

$900.99 x 6.75% = 60.82 (tax)
$900.99 + $60.82 = $961.81 total cost.

Estimate the product. Round each factor to the nearest whole number, and then multiply.

0.9 × 1.084

Answers

0.10 x 2.000 = 0.2

0.9 = 0.10

1.084=2.000

A car travels 470.7 kilometers on 52.3 liters of gas. How much gas will it need to go 345.6 kilometers?

Answers

Answer:

38.4[litres].

Step-by-step explanation:

[tex]1. \ the \ rule \ \frac{470.7[km]}{52.3[l]} =\frac{345.6[km]}{x};[/tex]

[tex]2. \ x=\frac{345.6*52.3}{470.7}=38.4[l].[/tex]

Please help with the steps to get the answer. Thank you.
15^(4x-8 )= 1

Answers

[tex]15^{4x-8} =1\\\\\implies 15^{4x-8} = 15^0\\\\\implies 4x -8 = 0\\\\\implies 4x = 8\\\\\implies x = \dfrac 84\\\\\implies x =2[/tex]

how many integers between 100 and 999 (inclusive) have distinct digits

Answers

Answer:

648

Step-by-step explanation:

Running this in Python, with the code as follows,

import math

cur_numbers = [0] * 3

num = 0

for i in range(100, 1000):

   cur_numbers[2] = i % 10

   i = math.floor(i/10)

   cur_numbers[1] = i % 10

   i = math.floor(i/10)

   cur_numbers[0] = i % 10

   if(len(set(cur_numbers)) == 3):

       num += 1

       print(cur_numbers)

       

print(num), we get 648 as our answer.

Another way to solve this is as follows:

There are 9 possibilities for the hundreds digit (1-9). Then, there are 10 possibilities for the tens digit, but we subtract 1 because it can't be the 1 same digit as the hundreds digit. For the ones digit, there are 10 possibilities, but we subtract 1 because it can't be the same as the hundreds digit and another 1 because it can't be the same as the tens digit. Multiplying these out, we have

9 possibilities for the hundreds digit x 9 possibilities for the tens digit x 8 possibilities for the ones digit  = 648

How do you turn 48% in to a decimal?​

Answers

Divide 48 by 100 to get it into decimal form, which is 48.

Answer:

0.48

Step-by-step explanation:

Since a percent is ALWAYS a part of the number 1, this makes it to where you must multiply by 100 in order to convert a percent into a decimal. In this case, 48%(100) is 0.48.

what is twenty-five hundred-thousandths in decimal form

Answers

Answer:

5.620

Step-by-step explanation:

I hope this helps you

Answer:

0.00025

Step-by-step explanation:

Here is a example

y varies directly as x . when x=3 , then y=12 . find y when x=20.

Answers

Answer:

Congress. would equal 80 due to x being worth 1/4 of y's total.

The price of 50 litres of petrol is £36, find the price of each litre of petrol.

Answers

50/36 = 1.39 per litre (or 1.86 dollars for those in the United States)

Choose the equations that are not linear equations.



X/2 -y*3 = 1
O - x-y= 2.
x2 + y=4
x= 5

Answers

Answer:

#2 and #4

Step-by-step explanation:

Anything with a variable squared is not linear

Kiara bought fabric to make a dress and a sewing machine. The total cost of her purchase, $80.50, included both the cost of her sewing machine

Write an equation to determine the cost of fabric per foot

find the cost of fabric per foot

Answers

The cost is of fabric per foot 40.25$
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